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71 lines
2.2 KiB
C++
71 lines
2.2 KiB
C++
#include <cmath>
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#include "ellipsoid.h"
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#include "lambertazimuthal.h"
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#define sin2(x) (sin(x) * sin(x))
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#define sqr(x) ((x) * (x))
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LambertAzimuthal::LambertAzimuthal(const Ellipsoid *ellipsoid,
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double latitudeOrigin, double longitudeOrigin, double falseEasting,
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double falseNorthing)
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{
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double lat0 = deg2rad(latitudeOrigin);
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_falseEasting = falseEasting;
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_falseNorthing = falseNorthing;
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_lon0 = deg2rad(longitudeOrigin);
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_a = ellipsoid->radius();
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_es = ellipsoid->es();
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_e = sqrt(_es);
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double q0 = (1.0 - _es) * ((sin(lat0) / (1.0 - _es * sin2(lat0)))
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- ((1.0/(2.0*_e)) * log((1.0 - _e * sin(lat0)) / (1.0 + _e
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* sin(lat0)))));
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_qP = (1.0 - _es) * ((1.0 / (1.0 - _es)) - ((1.0/(2.0*_e))
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* log((1.0 - _e) / (1.0 + _e))));
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_beta0 = asin(q0 / _qP);
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_Rq = _a * sqrt(_qP / 2.0);
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_D = _a * (cos(lat0) / sqrt(1.0 - _es * sin2(lat0))) / (_Rq * cos(_beta0));
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}
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PointD LambertAzimuthal::ll2xy(const Coordinates &c) const
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{
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double lon = deg2rad(c.lon());
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double lat = deg2rad(c.lat());
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double q = (1.0 - _es) * ((sin(lat) / (1.0 - _es * sin2(lat)))
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- ((1.0/(2.0*_e)) * log((1.0 - _e * sin(lat)) / (1.0 + _e
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* sin(lat)))));
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double beta = asin(q / _qP);
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double B = _Rq * sqrt(2.0 / (1.0 + sin(_beta0) * sin(beta) + (cos(_beta0)
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* cos(beta) * cos(lon - _lon0))));
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double x = _falseEasting + ((B * _D) * (cos(beta) * sin(lon - _lon0)));
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double y = _falseNorthing + (B / _D) * ((cos(_beta0) * sin(beta))
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- (sin(_beta0) * cos(beta) * cos(lon - _lon0)));
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return PointD(x, y);
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}
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Coordinates LambertAzimuthal::xy2ll(const PointD &p) const
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{
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double es4 = _es * _es;
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double es6 = _es * es4;
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double rho = sqrt(sqr((p.x() - _falseEasting) / _D) + sqr(_D * (p.y()
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- _falseNorthing)));
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double C = 2.0 * asin(rho / (2.0*_Rq));
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double betaS = asin((cos(C) * sin(_beta0)) + ((_D * (p.y() -_falseNorthing)
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* sin(C) * cos(_beta0)) / rho));
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double lon = _lon0 + atan((p.x() - _falseEasting) * sin(C) / (_D * rho
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* cos(_beta0) * cos(C) - sqr(_D) * (p.y() - _falseNorthing) * sin(_beta0)
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* sin(C)));
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double lat = betaS + ((_es/3.0 + 31.0*es4/180.0 + 517.0*es6/5040.0)
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* sin(2.0*betaS)) + ((23.0*es4/360.0 + 251.0*es6/3780.0) * sin(4.0*betaS))
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+ ((761.0*es6/45360.0)*sin(6.0*betaS));
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return Coordinates(rad2deg(lon), rad2deg(lat));
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}
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